Computer Science ›› 2018, Vol. 45 ›› Issue (6): 1-8.doi: 10.11896/j.issn.1002-137X.2018.06.001

• Surveys •     Next Articles

Survey on Hidden Subgroup Problem

DAI Wen-jing, YUAN Jia-bin   

  1. College of Computer Science and Technology,Nanjing University of Aeronautics & Astronautics,Nanjing 211106,China
  • Received:2017-05-09 Online:2018-06-15 Published:2018-07-24

Abstract: After Shor has presented an effective quantum algorithm for factoring of large integer,quantum computation forces us to re-examine the existing cryptosystems.Hidden subgroup problem is the generalization of quantum computation in group structure,it implicits that more difficult problems might be solved by considering various groups and functions to find new algorithms which are exponentially faster than their classical counterparts.The abelian hidden subgroup problem research has formed a relatively unified framework,while the non-abelian hidden subgroup problem research is always alive.The dihedral hidden subgroup problem may break the cryptosystems of the unique shortest vector problem based on the lattice and the graph isomorphism problem can be reduced to the symmetric hidden subgroup problem.The hidden subgroup problem was summarized to attract more researchers.Finally,this paper provided a suggestion for the direction of future research.

Key words: Quantum computation, Hidden subgroup problem, Abelian group, Dihedral group, Unique shortest vector problem, Symmetric group

CLC Number: 

  • TP309.2
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